Pre-Calculus Homework Solutions 119

Pre-Calculus Homework Solutions 119 - 2 Sample answer 5...

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121 Chapter 5 2. Sample answer: 3. Sample answer: An altitude and angle bisector of a triangle are the same segment in an equilateral triangle. 4. Find an equation of the perpendicular bisector of AB . The slope of AB is 1 6 , so the slope of the perpendicular bisector is 6. The midpoint of AB is 0, 5 2 . y y 1 ¬ m ( x x 1 ) y 5 2 ¬ 6( x 0) y 5 2 ¬ 6 x y ¬ 6 x 5 2 Find an equation of the perpendicular bisector of BC . The slope of BC is 3, so the slope of the perpendicular bisector of BC is 1 3 . The midpoint of BC is (2, 1). y y 1 ¬ m ( x x 1 ) y ( 1) ¬ 1 3 ( x 2) y 1 ¬ 1 3 x 2 3 y ¬ 1 3 x 1 3 Solve a system of equations to find the point of intersection of the perpendicular bisectors. Find x . y ¬ 6 x 5 2 1 3 x 1 3 ¬ 6 x 5 2 2 x 2 ¬ 36 x 15 17 ¬ 38 x 1 3 7 8 ¬ x Replace x with 1 3 7 8 in one of the equations to find the y -coordinate. y ¬ 6 1 3 7 8 5 2 y ¬ 3 7 8 The coordinates of the circumcenter of ABC are 1 3 7 8 , 3 7 8 . 5. Given: XY XZ YM and ZN are medians. Prove: YM ZN Proof: 6. Find x . TQ ¬ TR 2 x ¬ 8 x ¬ 4 Find y . PT ¬ TR 3 y 1 ¬ 8 3 y ¬ 9 y ¬ 3 Find z . Line bisects PR , so z 4 7, or z 3. Pages 243–245 Practice and Apply
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